Question: Solve for $x$ and $y$ using elimination. ${5x+2y = 33}$ ${-4x-2y = -30}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {5x+2y = 33}\thinspace$ to find $y$ ${5}{(3)}{ + 2y = 33}$ $15+2y = 33$ $15{-15} + 2y = 33{-15}$ $2y = 18$ $\dfrac{2y}{{2}} = \dfrac{18}{{2}}$ ${y = 9}$ You can also plug ${x = 3}$ into $\thinspace {-4x-2y = -30}\thinspace$ and get the same answer for $y$ : ${-4}{(3)}{ - 2y = -30}$ ${y = 9}$